A126388 Denominators in a series for the "alternating Euler constant" log(4/Pi).

2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 23, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 78, 79, 80, 81, 86, 87, 90, 91, 92

Offset

2,1

Comments

All n > 1 such that (# of 1's) != (# of 0's) in the base 2 expansion of floor(n/2). The numerators of the series are A126389.

Links

Table of n, a(n) for n=2..72.

Jonathan Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, arXiv:math/0211148 [math.CA], 2002-2004.

Jonathan Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005), 61-65.

Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi), arXiv:math/0508042 [math.NT], 2005.

Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi), Additive Number Theory, Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (D. Chudnovsky and G. Chudnovsky, eds.), Springer, 2010, pp. 331-340.

Eric Weisstein's MathWorld, Digit Count.

Formula

log(4/Pi) = 1/2 - 1/3 + 2/6 - 2/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 3/14 - 3/15 - 2/16 + 2/17 + 2/22 - ...

Example

floor(13/2) = 6 = 110 base 2, which has (# of 1's) = 2 != 1 = (#
of 0's), so 13 is a member.

Mathematica

b[n_] := DigitCount[n, 2, 1] - DigitCount[n, 2, 0]; L = {}; Do[If[b[Floor[n/2]] != 0, L = Append[L, n]], {n, 2, 100}]; L

Crossrefs

Complementary to A066879.

Cf. A037861, A094640, A094641, A110625, A110626, A126389.

Sequence in context: A088573 A181514 A225755 * A039247 A371292 A039189

Adjacent sequences: A126385 A126386 A126387 * A126389 A126390 A126391

Keyword

base,nonn

Author

Jonathan Sondow, Jan 01 2007

Status

approved